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A345951
a(n) = 1 if A002034(n), the smallest positive integer k such that n divides k!, is larger than A006530(n), the greatest prime factor of n, otherwise 0.
3
0, 0, 0, 1, 0, 0, 0, 1, 1, 0, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 1, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1
OFFSET
1
COMMENTS
a(n) = 1 if n does not divide A000142(A006530(n)), and 0 otherwise.
a(n) = 1 if A002034(n), the smallest positive integer k such that n divides k!, is composite, 0 otherwise.
FORMULA
a(n) = 1 if A345940(n) > 0, otherwise 0.
a(n) <= A345952(n) for all n >= 1.
PROG
(PARI)
A006530(n) = if(1==n, n, my(f=factor(n)); f[#f~, 1]);
A345951(n) = !!(A006530(n)!%n);
(PARI)
A002034(n) = if(1==n, n, my(s=factor(n)[, 1], k=s[#s], f=Mod(k!, n)); while(f, f*=k++); (k)); \\ After code in A002034.
A345951(n) = (A006530(n) < A002034(n));
(PARI) A345951(n) = ((n>1)&&!isprime(A002034(n)));
CROSSREFS
Characteristic function of A057109.
Sequence in context: A023969 A060039 A319710 * A345952 A359466 A359467
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jul 04 2021
STATUS
approved